Table of Contents

Maximum and Minimum Values; Usual Methods for Proving Inequalities; Common Techniques for Proving Inequalities; Arithmetic and Geometric Sequences; Arithmetic Sequences of Higher Order; Sequence Summation; Synthetic Problems for Sequences; Coordinates Systems; Straight Lines; Circles; Ellipses; Hyperbolas; Parabolas; Parametric Equations; Families of Curves; Derivatives; Mathematical Induction (I); Complex Numbers; Geometric Meaning of Complex Operations; Mean Value Inequalities; Cauchy Inequality; Rearrangement Inequalities; Convex Functions and Jensen's Inequality; Recursive Sequences; Periodic Sequences; Polar Coordinates; Analytic Method for Plane Geometry; Synthetic Problems for Complex Numbers; Mathematical Induction (II); Proof by Contradiction; Construction Method;

About the Author

Shi-Xiong Liu, Principal of The Associated High School of South China Normal University, Mathematics Grand Grade Teacher, Senior Coach of The Chinese Mathematical Olympiad.